Probability: Sibling Pairs

[tvd04c]

A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

a. 3/40,000
b. 1/3,600
c. 9/2,000
d. 1/60
e. 1/15

According to the OG 11th edition, the answer is the probability of selecting sibling pairs in the junior class multiplied by the probability of selecting a match in the senior class. 60/1,000 x 1/800 = 3/40,000.

My question is why isn't the answer:
the probability of selecting sibling pairs in the junior class AND the probability of selecting a match in the senior class
OR
the probability of selecting a sibling a pair from the senior class AND the probability of selecting a match in the junior class.

(60/1,000 x 1/800) + (60/800 x 1/1,000) = 3/20,000.

[GMATGuruNY]

A certain junior class has 1,000 students and a certain senior class has 800 students. Among these students, there are 60 sibling pairs, each consisting of 1 junior and 1 senior. If 1 student is to be selected at random from each class, what is the probability that the 2 students selected will be a sibling pair?

a. 3/40,000
b. 1/3,600
c. 9/2,000
d. 1/60
e. 1/15

According to the OG 11th edition, the answer is the probability of selecting sibling pairs in the junior class multiplied by the probability of selecting a match in the senior class. 60/1,000 x 1/800 = 3/40,000.

My question is why isn't the answer:
the probability of selecting sibling pairs in the junior class AND the probability of selecting a match in the senior class
OR
the probability of selecting a sibling a pair from the senior class AND the probability of selecting a match in the junior class.

(60/1,000 x 1/800) + (60/800 x 1/1,000) = 3/20,000.

You're double-counting the sibling pairs.
Since each pair consists of 1 junior and 1 senior, it doesn't matter whether we select first from the junior class and then from the senior class or first from the senior class and then from the junior class: either way, we'll be counting the same sibling pairs.

Another approach:

P(sibling pair) = (total number of sibling pairs)/(total number of possible pairs).

Total number of possible pairs:
There are 1000 juniors and 800 seniors.
Total number of ways to combine 1 junior with 1 senior = 1000*800 = 800,000.

Total number of sibling pairs = 60.

P(sibling pair) = 60/800,000 = 3/40,000.

The correct answer is A.